The present invention relates to a method for producing the textures characterizing a geological structure on a support and, more particularly, a method for obtaining a representative topological map of the textures characterizing a geological structure from an image of an area of said geological structure.
Electrical images of well boreholes as obtained, for example, via FMI (Fullbore Formation MicroImage) and/or FMS (Formation Micro Scanner) tools which are developed by the Schlumberger Company, are of interest to the petroleum industry for the wealth of information which they contain. These images are used nearly exclusively by structuralists for the fine measurement of the geometric characteristics of the bedding and fracture planes in boreholes.
The FMS and FMI tools serve to acquire electrical images from measurements of the local electrical conductivity of the well borehole and utilize four articulated arms, each equipped with a pad and a flap (accompanied pad). Each pad comprises 24 electrodes, for example, and is held against the well borehole by a mechanical system, throughout the image acquisition time.
An electrical image is a view of the well borehole and, when the borehole is open, presents a horizontal axis representing the azimuthal distribution of the pad electrodes, and a vertical axis corresponding to the depth (elevation) of the tool in the borehole. The image of the well borehole is thus formed, for example, of 24 columns (one column per electrode) and several thousand lines, each pixel of the image having a size of about 2.5 mM.sup.2. The electrical image is analyzed in terms of planar heterogeneities and point heterogeneities. The planar heterogeneity is used to analyze the bedding planes and the fracture planes of the geological medium which are intersected by the stratification. The rest of the electrical image represents the variations which are associated with variations in the petrophysical parameters (porosity) or with variations in sedimnentological parameters (bioturbations etc).
The analysis and automatic segmentation of the texture of the electrical images of the well borehole have been undertaken. However, the operations performed for the above purpose raise problems from the standpoint of discrimination. Discrimination is the process of identifying typical textures observable in the electrical image of the borehole, making a scan of the attributes to characterize them, and finally, in the attribute space, determining hyperplanes to discriminate them.
J. F. Rivest proposes to use a mathematical morphology and a hierarchical classification (`Analyse automatique d'images geologiques et l'application de la morphologie mathematique aux images diagraphies`, PhD Thesis, Ecole Nationale Superieure des Mines de Paris, 1992).
Harris et al use co occurrence matrices with a classification by neural networks for discrimination (`The identification of lithofacies types in geological imagery using neural networks`, Eurocaipep 93, 20-22/09/1993), whereas, by using the texture energies defined by Laws (Goal, Directed Texture Segmentation, Technical Note 334, Artificial Intelligence Center, SRI International, Meulo Park, 29 p.), Luthi proposes an analysis by principal components to compress said energies (`Textural segmentation of digital rock images into bedding units using texture energy and cluster, Mathematical Geology, Vol. 26, No. 2, pp. 181-198).
Gagalowicz tried to explain that a texture is a quantitative measurement for describing the content of a region in an image and that it is related to visual perception. He translated this via the `invariance by translation` concept, i.e., the observation of a texture leaves the same visual impression irrespective of the portion of the texture observed. He also defined the `textural resolution`, which is the minimum size of the observation window under which the textural parameters are no longer invariant by translation. (`Vers un modele de textures`, PhD Thesis, Universite de Paris VI, 1983).
Gagalowicz and Ma (`Natural texture synthesis with the control of correlation and histogram`, 3rd Scandinavian Conference on Image Analysis, Copenhagen, Denmark, July 1983) proposed a model which is defined by the moments of the first and second orders (histogram and autocovariance) and demonstrated that this model can be used to represent a vast class of natural textures. In fact, the histogram helps to preserve the textural contrast, while the autocovariance provides the data on the orientation and size of the texture grains.
The histogram (H) and autocovariance (M.sub.2) are given by equations (1) and (2): ##EQU1## .DELTA.=(.DELTA.x,.DELTA.y) is a translation of the plane; N is the total number of image pixels;
X.sub.i and X.sub.i +.DELTA. are the values of the luminous intensity of the pixels in position i and i+.DELTA. of the texture; PA1 l is one of the L possible luminances; and PA1 .delta. is the Kronecker indicia, .delta.(x)=1, if x=0 and .delta.(x)=0 everywhere else. PA1 images are produced characterizing the sedimentology of said medium; PA1 at every point of each image, and in a spatial domain about said point, parameters corresponding to the nature of said images are estimated in order to determine the texture vector for each of said points in such a way as to obtain a set of texture vectors; PA1 from said set, texture vectors are selected which are representative of the characteristic textures of said geological medium; PA1 a neural network is used formed of cells distributed in two dimensions which comprises as many cells as characteristic textures, and a learning process is applied to said neural network via said selected texture vectors, in order to obtain a final topological map of said characteristic textures of the geological medium.
Since M.sub.2 (.DELTA.)=M.sub.2 (-.DELTA.), the total number of translations to observe the texture is: EQU M=Nx*Ny/2-1, (3)
where Nx and Ny are the sizes of the control texture in X/Y coordinates, which are adjusted according to the structure and the texture concerned.
The number of parameters of the texture model defmed by the histogram H and the autocovariances M.sub.2 (.DELTA.) is hence: EQU D.sub.2 =L+M (4)
However, this model has a relatively small number of parameters compared with the other stochastic models such as those of the cooccurrence matrices, and does not always help to describe the set of textures visible on the electrical images.